BELFEM 0.9.0
Berkeley Lab Finite Element Framework
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fn_intpoints_gauss_penta40.hpp
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1/*
2 * BELFEM -- The Berkeley Lab Finite Element Framework
3 * Copyright (c) 2026, The Regents of the University of California,
4 * through Lawrence Berkeley National Laboratory (subject to receipt of any required
5 * approvals from the U.S. Dept. of Energy). All rights reserved.
6 *
7 * Developers: Christian Messe, Gregory Giard
8 *
9 * See the top-level LICENSE file for the complete license and disclaimer.
10 */
11
12#ifndef BELFEM_FN_INTPOINTS_GAUSS_PENTA40_HPP
13#define BELFEM_FN_INTPOINTS_GAUSS_PENTA40_HPP
14
15#include "typedefs.hpp"
16#include "cl_Vector.hpp"
17#include "cl_Matrix.hpp"
18
19namespace belfem
20{
21 namespace integration
22 {
23// ----------------------------------------------------------------------------
24
25 // source: 10.1016/j.compfluid.2013.01.002
26 inline void
27 gauss_penta40(
28 Vector< real > & aWeights,
29 Matrix< real > & aPoints )
30 {
31 aPoints.set_size( 3, 40 );
32
33 aPoints( 0, 0 ) = 0.33333333333333;
34 aPoints( 1, 0 ) = 0.33333333333333;
35 aPoints( 2, 0 ) = 0.00000000000000;
36
37 aPoints( 0, 1 ) = 0.18871803775194;
38 aPoints( 1, 1 ) = 0.62256392449612;
39 aPoints( 2, 1 ) = 0.00000000000000;
40
41 aPoints( 0, 2 ) = 0.18871803775194;
42 aPoints( 1, 2 ) = 0.18871803775194;
43 aPoints( 2, 2 ) = 0.00000000000000;
44
45 aPoints( 0, 3 ) = 0.62256392449612;
46 aPoints( 1, 3 ) = 0.18871803775194;
47 aPoints( 2, 3 ) = 0.00000000000000;
48
49 aPoints( 0, 4 ) = 0.42452658418154;
50 aPoints( 1, 4 ) = 0.15094683163691;
51 aPoints( 2, 4 ) = 0.73970515364641;
52
53 aPoints( 0, 5 ) = 0.42452658418154;
54 aPoints( 1, 5 ) = 0.15094683163691;
55 aPoints( 2, 5 ) = -0.73970515364641;
56
57 aPoints( 0, 6 ) = 0.42452658418154;
58 aPoints( 1, 6 ) = 0.42452658418154;
59 aPoints( 2, 6 ) = 0.73970515364641;
60
61 aPoints( 0, 7 ) = 0.42452658418154;
62 aPoints( 1, 7 ) = 0.42452658418154;
63 aPoints( 2, 7 ) = -0.73970515364641;
64
65 aPoints( 0, 8 ) = 0.15094683163691;
66 aPoints( 1, 8 ) = 0.42452658418154;
67 aPoints( 2, 8 ) = 0.73970515364641;
68
69 aPoints( 0, 9 ) = 0.15094683163691;
70 aPoints( 1, 9 ) = 0.42452658418154;
71 aPoints( 2, 9 ) = -0.73970515364641;
72
73 aPoints( 0, 10 ) = 0.05578045134845;
74 aPoints( 1, 10 ) = 0.88843909730309;
75 aPoints( 2, 10 ) = 0.52119188479234;
76
77 aPoints( 0, 11 ) = 0.05578045134845;
78 aPoints( 1, 11 ) = 0.88843909730309;
79 aPoints( 2, 11 ) = -0.52119188479234;
80
81 aPoints( 0, 12 ) = 0.05578045134845;
82 aPoints( 1, 12 ) = 0.05578045134845;
83 aPoints( 2, 12 ) = 0.52119188479234;
84
85 aPoints( 0, 13 ) = 0.05578045134845;
86 aPoints( 1, 13 ) = 0.05578045134845;
87 aPoints( 2, 13 ) = -0.52119188479234;
88
89 aPoints( 0, 14 ) = 0.88843909730309;
90 aPoints( 1, 14 ) = 0.05578045134845;
91 aPoints( 2, 14 ) = 0.52119188479234;
92
93 aPoints( 0, 15 ) = 0.88843909730309;
94 aPoints( 1, 15 ) = 0.05578045134845;
95 aPoints( 2, 15 ) = -0.52119188479234;
96
97 aPoints( 0, 16 ) = 0.72439742063389;
98 aPoints( 1, 16 ) = 0.06040303157525;
99 aPoints( 2, 16 ) = 0.96784776572476;
100
101 aPoints( 0, 17 ) = 0.72439742063389;
102 aPoints( 1, 17 ) = 0.06040303157525;
103 aPoints( 2, 17 ) = -0.96784776572476;
104
105 aPoints( 0, 18 ) = 0.21519954779086;
106 aPoints( 1, 18 ) = 0.06040303157525;
107 aPoints( 2, 18 ) = 0.96784776572476;
108
109 aPoints( 0, 19 ) = 0.21519954779086;
110 aPoints( 1, 19 ) = 0.06040303157525;
111 aPoints( 2, 19 ) = -0.96784776572476;
112
113 aPoints( 0, 20 ) = 0.06040303157525;
114 aPoints( 1, 20 ) = 0.21519954779086;
115 aPoints( 2, 20 ) = 0.96784776572476;
116
117 aPoints( 0, 21 ) = 0.06040303157525;
118 aPoints( 1, 21 ) = 0.21519954779086;
119 aPoints( 2, 21 ) = -0.96784776572476;
120
121 aPoints( 0, 22 ) = 0.06040303157525;
122 aPoints( 1, 22 ) = 0.72439742063389;
123 aPoints( 2, 22 ) = 0.96784776572476;
124
125 aPoints( 0, 23 ) = 0.06040303157525;
126 aPoints( 1, 23 ) = 0.72439742063389;
127 aPoints( 2, 23 ) = -0.96784776572476;
128
129 aPoints( 0, 24 ) = 0.21519954779086;
130 aPoints( 1, 24 ) = 0.72439742063389;
131 aPoints( 2, 24 ) = 0.96784776572476;
132
133 aPoints( 0, 25 ) = 0.21519954779086;
134 aPoints( 1, 25 ) = 0.72439742063389;
135 aPoints( 2, 25 ) = -0.96784776572476;
136
137 aPoints( 0, 26 ) = 0.72439742063389;
138 aPoints( 1, 26 ) = 0.21519954779086;
139 aPoints( 2, 26 ) = 0.96784776572476;
140
141 aPoints( 0, 27 ) = 0.72439742063389;
142 aPoints( 1, 27 ) = 0.21519954779086;
143 aPoints( 2, 27 ) = -0.96784776572476;
144
145 aPoints( 0, 28 ) = 0.65229256105648;
146 aPoints( 1, 28 ) = 0.02175201894973;
147 aPoints( 2, 28 ) = 0.41341132937202;
148
149 aPoints( 0, 29 ) = 0.65229256105648;
150 aPoints( 1, 29 ) = 0.02175201894973;
151 aPoints( 2, 29 ) = -0.41341132937202;
152
153 aPoints( 0, 30 ) = 0.32595541999379;
154 aPoints( 1, 30 ) = 0.02175201894973;
155 aPoints( 2, 30 ) = 0.41341132937202;
156
157 aPoints( 0, 31 ) = 0.32595541999379;
158 aPoints( 1, 31 ) = 0.02175201894973;
159 aPoints( 2, 31 ) = -0.41341132937202;
160
161 aPoints( 0, 32 ) = 0.02175201894973;
162 aPoints( 1, 32 ) = 0.32595541999379;
163 aPoints( 2, 32 ) = 0.41341132937202;
164
165 aPoints( 0, 33 ) = 0.02175201894973;
166 aPoints( 1, 33 ) = 0.32595541999379;
167 aPoints( 2, 33 ) = -0.41341132937202;
168
169 aPoints( 0, 34 ) = 0.02175201894973;
170 aPoints( 1, 34 ) = 0.65229256105648;
171 aPoints( 2, 34 ) = 0.41341132937202;
172
173 aPoints( 0, 35 ) = 0.02175201894973;
174 aPoints( 1, 35 ) = 0.65229256105648;
175 aPoints( 2, 35 ) = -0.41341132937202;
176
177 aPoints( 0, 36 ) = 0.32595541999379;
178 aPoints( 1, 36 ) = 0.65229256105648;
179 aPoints( 2, 36 ) = 0.41341132937202;
180
181 aPoints( 0, 37 ) = 0.32595541999379;
182 aPoints( 1, 37 ) = 0.65229256105648;
183 aPoints( 2, 37 ) = -0.41341132937202;
184
185 aPoints( 0, 38 ) = 0.65229256105648;
186 aPoints( 1, 38 ) = 0.32595541999379;
187 aPoints( 2, 38 ) = 0.41341132937202;
188
189 aPoints( 0, 39 ) = 0.65229256105648;
190 aPoints( 1, 39 ) = 0.32595541999379;
191 aPoints( 2, 39 ) = -0.41341132937202;
192
193 aWeights.set_size( 40 );
194 aWeights( 0 ) = 0.04678131245277;
195 aWeights( 1 ) = 0.06992801416159;
196 aWeights( 2 ) = 0.06992801416159;
197 aWeights( 3 ) = 0.06992801416159;
198 aWeights( 4 ) = 0.04816594861924;
199 aWeights( 5 ) = 0.04816594861924;
200 aWeights( 6 ) = 0.04816594861924;
201 aWeights( 7 ) = 0.04816594861924;
202 aWeights( 8 ) = 0.04816594861924;
203 aWeights( 9 ) = 0.04816594861924;
204 aWeights( 10 ) = 0.01948499604627;
205 aWeights( 11 ) = 0.01948499604627;
206 aWeights( 12 ) = 0.01948499604627;
207 aWeights( 13 ) = 0.01948499604627;
208 aWeights( 14 ) = 0.01948499604627;
209 aWeights( 15 ) = 0.01948499604627;
210 aWeights( 16 ) = 0.00933216244754;
211 aWeights( 17 ) = 0.00933216244754;
212 aWeights( 18 ) = 0.00933216244754;
213 aWeights( 19 ) = 0.00933216244754;
214 aWeights( 20 ) = 0.00933216244754;
215 aWeights( 21 ) = 0.00933216244754;
216 aWeights( 22 ) = 0.00933216244754;
217 aWeights( 23 ) = 0.00933216244754;
218 aWeights( 24 ) = 0.00933216244754;
219 aWeights( 25 ) = 0.00933216244754;
220 aWeights( 26 ) = 0.00933216244754;
221 aWeights( 27 ) = 0.00933216244754;
222 aWeights( 28 ) = 0.01879525230824;
223 aWeights( 29 ) = 0.01879525230824;
224 aWeights( 30 ) = 0.01879525230824;
225 aWeights( 31 ) = 0.01879525230824;
226 aWeights( 32 ) = 0.01879525230824;
227 aWeights( 33 ) = 0.01879525230824;
228 aWeights( 34 ) = 0.01879525230824;
229 aWeights( 35 ) = 0.01879525230824;
230 aWeights( 36 ) = 0.01879525230824;
231 aWeights( 37 ) = 0.01879525230824;
232 aWeights( 38 ) = 0.01879525230824;
233 aWeights( 39 ) = 0.01879525230824;
234 }
235// ----------------------------------------------------------------------------
236 } /* namespace integration */
237} /* namespace belfem */
238
239#endif //BELFEM_FN_INTPOINTS_GAUSS_PENTA40_HPP
cl_Matrix.hpp
cl_Vector.hpp
belfem::Matrix::set_size
void set_size(const size_t aNumRows, const size_t aNumCols)
Definition cl_AR_Matrix.hpp:186
belfem::Vector::set_size
void set_size(const size_t aNumRows)
change the size of the vector
Definition cl_AR_Vector.hpp:237
belfem::integration
Definition fn_intpoints.cpp:576
belfem::integration::gauss_penta40
void gauss_penta40(Vector< real > &aWeights, Matrix< real > &aPoints)
Definition fn_intpoints_gauss_penta40.hpp:27
belfem
USER GUIDES:
Definition cl_Capacitor.cpp:16